R vs SAS Skewness/Kurtosis
Skewness Comparison
The following table shows the types of Skewness, the capabilities of each language, and whether or not the results from each language match.
| Analysis | Supported in R | Supported in SAS | Results Match | Notes |
|---|---|---|---|---|
| Skewness, Type 1 | Yes | Yes | Yes | In e1071, use type = 1.In SAS use vardef = N. |
| Skewness, Type 2 | Yes | Yes | Yes | In e1071, use type = 2.In SAS use vardef = DF.procs and sasLM use defaults. |
| Skewness, Type 3 | Yes | No | NA | In e1071, use type = 3.Not supported in SAS. |
Note that the SAS default is Type 2.
Kurtosis Comparison
The following table shows the types of Kurtosis, the capabilities of each language, and whether or not the results from each language match.
| Analysis | Supported in R | Supported in SAS | Results Match | Notes |
|---|---|---|---|---|
| Kurtosis, Type 1 | Yes | Yes | Yes | In e1071, use type = 1.In SAS use vardef = N. |
| Kurtosis, Type 2 | Yes | Yes | Yes | In e1071, use type = 2.In SAS use vardef = DF.procs and sasLM use defaults. |
| Kurtosis, Type 3 | Yes | No | NA | In e1071, use type = 3.Not supported in SAS. |
| Kurtosis, Pearson’s | Yes | No | NA | Use moments in R. Not supported in SAS. |
Note that the SAS default is Type 2.
Comparison Results
Skewness
Here is a table of Skewness comparison values between the four R packages examined and SAS:
| Statistic | e1071 | moments | procs | sasLM | SAS | Match | Notes |
|---|---|---|---|---|---|---|---|
| Skewness, Type 1 | 0.9054442 | 0.9054442 | NA | NA | 0.9054442 | Yes | |
| Skewness, Type 2 | 1.009318 | NA | 1.009318 | 1.009318 | 1.0093179 | Yes | |
| Skewness, Type 3 | 0.8164261 | NA | NA | NA | NA | NA | Type 3 not supported in SAS |
Kurtosis
Here is a table of Kurtosis comparison values between the four R packages examined and SAS:
| Statistic | e1071 | moments | procs | sasLM | SAS | Match | Notes |
|---|---|---|---|---|---|---|---|
| Kurtosis, Type 1 | -0.5833411 | NA | NA | NA | -0.5833411 | Yes | |
| Kurtosis, Type 2 | -0.2991564 | NA | -0.2991564 | -0.2991564 | -0.2991564 | Yes | |
| Kurtosis, Type 3 | -0.8948216 | NA | NA | NA | NA | NA | Type 3 not supported in SAS |
| Kurtosis, Pearson’s | NA | 2.416659 | NA | NA | NA | NA | Pearson’s not supported in SAS |
Summary and Recommendation
SAS uses a “Type 2” Skewness and Kurtosis by default. The same Type 2 methodology is supported in at least three different R packages: e1071, procs and sasLM. To match the SAS default, use one of these three packages.
SAS also supports a “Type 1” Skewness and Kurtosis via the VARDEF = N option. This methodology is supported in the e1071 package. The moments package also supports Type 1 for Skewness.
For a “Type 3” methodology, use the e1071 package with type = 3. This is the only source of the Type 3 methodology in either SAS or R.
The Pearson’s method for Kurtosis is available in the moments package. This package appears to be the only source of the Pearson’s Kurtosis.
References
e1071 skewness(): https://www.rdocumentation.org/packages/e1071/versions/1.7-14/topics/skewness
e1071 kurtosis(): https://www.rdocumentation.org/packages/e1071/versions/1.7-14/topics/kurtosis
moments documentation: https://cran.r-project.org/web/packages/moments/moments.pdf
procs proc_means() documentation: https://procs.r-sassy.org/reference/proc_means.html
sasLM documentation: https://cran.r-project.org/web/packages/sasLM/sasLM.pdf
SAS PROC MEANS: https://documentation.sas.com/doc/en/pgmsascdc/9.4_3.5/proc/p0v0y1on1hbxukn0zqgsp5ky8hc0.htm